Finite Group Databasebeta

← #14675697

Subgroups — #14675697

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622277C211yesmaximal, characteristic
2C2×#10622277C211yesmaximal, characteristic
3C2×#10622280C211yesmaximal, characteristic
4C2×#10622279C211yesmaximal, characteristic
5C2×D11×#95C211yesmaximal, characteristic
6#13066878C211yesmaximal, characteristic, complemented
7#13066874C211yesmaximal, characteristic, complemented
8#13066871C211yesmaximal, characteristic, complemented
9#13066851C211yesmaximal, characteristic, complemented
10#13066847C211yesmaximal, characteristic, complemented
11#13066842C211yesmaximal, characteristic, complemented
12#13066840C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×#1443C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51#10622280—24no—
52#10622279—24no—
53#10622277—24no—
54#10622277—24no—
55D11×#95C418yescomplemented
56C24×D11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—41no—
86C22×C4×D11—41no—
87C22×C4×D11—41no—
88C22×C4×D11—41no—
89C22×C4×D11C2×C414yes—
90C22×C4×D11C2×C414yes—
91C22×C4×D11C2×C414yes—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4D414yes—
103C2×(C2×D11)⋊C4D414yes—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—41no—
109C2×Dic11⋊C4—41no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—22no—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11—41no—
115C2×C4×Dic11—41no—
116C11×#95—22no—
117C11×#95—22no—
118C11×#95—22no—
119C11×#95—22no—
120C11×#95—41no—
121C11×#95—41no—
122C11×#95C2×C414yes—
123C11⋊#95—22no—
124C11⋊#95—22no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95C2×C414yes—
138C11⋊#95C2×C414yes—
139C11⋊#95C2×C414yes—
140#13874—111nomaximal, Sylow
141C24×C11C2411yescharacteristic
142C23×D11—21no—
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11C22×C412yes—
151C23×D11C2×D412yes—
152C23×D11C2×D412yes—
153C23×D11#4112yes—
154C23×D11#4112yes—
155C23×D11#4112yes—
156C23×D11#4112yes—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11C22×C412yes—
202C22×C4×C11C22×C412yes—
203C22×C4×C11C22×C412yes—
204C22×C4×C11C2×D412yes—
205C22×C4×C11C2×D412yes—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11C22×C412yes—
247C22×Dic11C22×C412yes—
248C22×Dic11C22×C412yes—
249C22×Dic11C2×D412yes—
250C22×Dic11C2×D412yes—
251C22×Dic11#4112yes—
252C22×Dic11#4112yes—
253C22×Dic11#4112yes—
254C22×Dic11#4112yes—
255C2×C4×D11—28no—
256C2×C4×D11—28no—
257C2×C4×D11—28no—
258C2×C4×D11—28no—
259C2×C4×D11—28no—
260C2×C4×D11—28no—
261C2×C4×D11—28no—
262C2×C4×D11—44no—
263C2×C4×D11—44no—
264C2×C4×D11—44no—
265C2×C4×D11—44no—
266C2×C4×D11—44no—
267C2×C4×D11—44no—
268C2×C4×D11—44no—
269C2×C4×D11—44no—
270C2×C4×D11—44no—
271C2×C4×D11—44no—
272C2×C4×D11—44no—
273C2×C4×D11—44no—
274C2×C4×D11—44no—
275C2×C4×D11—44no—
276(C2×D11)⋊C4—28no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—44no—
279(C2×D11)⋊C4—44no—
280Dic11⋊C4—44no—
281Dic11⋊C4—44no—
282C4×Dic11—44no—
283C4×Dic11—44no—
284C2×#381—111no—
285C2×#381—111no—
286C2×#380—111no—
287C2×C4×C22⋊C4—111no—
288C22×#95—111no—
289#1443—111no—
290#1443D1111yescharacteristic, complemented
291#1442—111no—
292#1442—111no—
293#1436—111no—
294#1436—111no—
295#1434—111no—
296#1434—111no—
297C22⋊#95—111no—
298C22⋊#95—111no—
299C23×C11C23×C411yescharacteristic
300C23×C11C22×D411yescharacteristic
301C23×C11C22×D411yescharacteristic
302C23×C11C2×#4111yescharacteristic
303C23×C11C2×#4111yescharacteristic
304C23×C11C2×#4111yescharacteristic
305C23×C11C2×#4111yescharacteristic
306C23×C11C2×#4111yescharacteristic
307C23×C11C2×#4111yescharacteristic
308C23×C11C2×#4111yescharacteristic
309C23×C11C2×#4111yescharacteristic
310C23×C11H(5,𝔽2)11yescharacteristic
311C23×C11H(5,𝔽2)11yescharacteristic
312C23×C112−1+411yescharacteristic
313C23×C112−1+411yescharacteristic
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11#11714yes—
343C22×D11C4×D414yes—
344C22×D11C4×D414yes—
345C22×D11#12114yes—
346C22×D11#12314yes—
347C22×D11#12414yes—
348C22×D11#12614yes—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11#11714yes—
446C2×Dic11#11714yes—
447C4×D11—416no—
448C4×D11—416no—
449C4×D11—416no—
450C24×C4—111no—
451C24×C4—111no—
452C24×C4—111no—
453C22×C4⋊C4—111no—
454C22×C4⋊C4—111no—
455C22×C22⋊C4—111no—
456C22×C22⋊C4—111no—
457C22×C22⋊C4—111no—
458C22×C22⋊C4—111no—
459C22×C42—111no—
460C22×C42—111no—
461#381—224no—
462#381—224no—
463#380—224no—
464C4×C22⋊C4—224no—
465C2×#95—111no—
466C2×#95—111no—
467C2×#95—111no—
468C2×#95—118no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95—111no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95C2×D1111yescharacteristic
484C2×#95C2×D1111yescharacteristic
485C2×#95C2×D1111yescharacteristic
486C2×#95C2×D1111yescharacteristic
487C2×#95C2×D1111yescharacteristic
488C2×#95C2×D1111yescharacteristic
489C2×#95C2×D1111yescharacteristic
490C22×C11C2×#11711yescharacteristic
491C22×C11C2×#11711yescharacteristic
492C22×C11C2×#11711yescharacteristic
493C22×C11C2×C4×D411yescharacteristic
494C22×C11C2×C4×D411yescharacteristic
495C22×C11#51811yescharacteristic
496C22×C11#51911yescharacteristic
497C22×C11C2×#12111yescharacteristic
498C22×C11C2×#12311yescharacteristic
499C22×C11C2×#12411yescharacteristic
500C22×C11C2×#12611yescharacteristic
501C22×C11#52911yescharacteristic
502C22×C11#52911yescharacteristic
503C22×C11#52911yescharacteristic
504C22×C11#52911yescharacteristic
505C22×C11#53911yescharacteristic
506C22×C11#53911yescharacteristic
507C22×C11#53911yescharacteristic
508C22×C11#53911yescharacteristic
509C22×C11#54611yescharacteristic
510C22×C11#54611yescharacteristic
511C22×C11#54611yescharacteristic
512C22×C11#54611yescharacteristic
513C22×C11#54711yescharacteristic
514C22×C11#54711yescharacteristic
515C22×C11#54711yescharacteristic
516C22×C11#54711yescharacteristic
517C22×C11#55111yescharacteristic
518C22×C11#55111yescharacteristic
519C22×C11#55111yescharacteristic
520C22×C11#55111yescharacteristic
521C22×C11#55211yescharacteristic
522C22×C11#55211yescharacteristic
523C22×C11#55211yescharacteristic
524C22×C11#55211yescharacteristic
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—24no—
530C2×D11—24no—
531C2×D11—24no—
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—24no—
535C2×D11—24no—
536C2×D11—24no—
537C2×D11—24no—
538C2×D11—24no—
539C2×D11#38818yes—
540C4×C11—42no—
541C4×C11—42no—
542C4×C11—42no—
543C4×C11—42no—
544C4×C11—42no—
545C4×C11—81no—
546C4×C11—81no—
547Dic11—24no—
548Dic11—24no—
549Dic11—42no—
550Dic11—42no—
551Dic11—42no—
552Dic11—81no—
553Dic11—81no—
554C25—111no—
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—111no—
560C23×C4—114no—
561C23×C4—114no—
562C23×C4—114no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4—222no—
566C23×C4—222no—
567C23×C4—222no—
568C23×C4—222no—
569C23×C4—222no—
570C23×C4—222no—
571C23×C4—222no—
572C23×C4—222no—
573C23×C4—222no—
574C23×C4—222no—
575C23×C4—222no—
576C23×C4—222no—
577C23×C4—222no—
578C23×C4—222no—
579C23×C4—441no—
580C23×C4—441no—
581C23×C4—441no—
582C23×C4—441no—
583C23×C4C22×D1111yescharacteristic
584C23×C4C22×D1111yescharacteristic
585C23×C4C22×D1111yescharacteristic
586C23×C4C22×D1111yescharacteristic
587C23×C4C22×D1111yescharacteristic
588C23×C4C22×D1111yescharacteristic
589C23×C4C22×D1111yescharacteristic
590C2×C4⋊C4—222no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—222no—
594C2×C4⋊C4—441no—
595C2×C4⋊C4—441no—
596C2×C22⋊C4—114no—
597C2×C22⋊C4—114no—
598C2×C22⋊C4—222no—
599C2×C22⋊C4—222no—
600C2×C22⋊C4—222no—
601C2×C22⋊C4—222no—
602C2×C22⋊C4—222no—
603C2×C22⋊C4—222no—
604C2×C22⋊C4—222no—
605C2×C22⋊C4—222no—
606C2×C22⋊C4—222no—
607C2×C22⋊C4—222no—
608C2×C42—222no—
609C2×C42—222no—
610C2×C42—222no—
611C2×C42—222no—
612C2×C42—441no—
613C2×C42—441no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—41no—
619#95—41no—
620#95—114no—
621#95—114no—
622#95—114no—
623#95—222no—
624#95—222no—
625#95—222no—
626#95—222no—
627#95—222no—
628#95—222no—
629#95—222no—
630#95—222no—
631#95—222no—
632#95—222no—
633#95—222no—
634#95—222no—
635#95—441no—
636#95—441no—
637#95C4×D1114yes—
638C2×C11#228311yescharacteristic
639C2×C11C2×#38811yescharacteristic
640C2×C11#231311yescharacteristic
641C2×C11#234211yescharacteristic
642C2×C11#234211yescharacteristic
643C2×C11#234411yescharacteristic
644C2×C11#234411yescharacteristic
645C2×C11#241911yescharacteristic
646C2×C11#241911yescharacteristic
647C2×C11#242511yescharacteristic
648C2×C11#242511yescharacteristic
649C2×C11#248811yescharacteristic
650C2×C11#248811yescharacteristic
651C2×C11#249311yescharacteristic
652C2×C11#249311yescharacteristic
653D11—28no—
654C24—112no—
655C24—112no—
656C24—112no—
657C24—112no—
658C24—112no—
659C24—112no—
660C24—112no—
661C24—221no—
662C24—221no—
663C24—221no—
664C24—221no—
665C24—221no—
666C24—221no—
667C24—221no—
668C24—221no—
669C24C23×D1111yescharacteristic
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—112no—
718C22×C4—112no—
719C22×C4—112no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—112no—
723C22×C4—228no—
724C22×C4—228no—
725C22×C4—228no—
726C22×C4—228no—
727C22×C4—228no—
728C22×C4—228no—
729C22×C4—228no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—221no—
761C22×C4—221no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—444no—
771C22×C4—444no—
772C22×C4—444no—
773C22×C4—444no—
774C22×C4—444no—
775C22×C4—444no—
776C22×C4—444no—
777C22×C4—444no—
778C22×C4—444no—
779C22×C4—444no—
780C22×C4—444no—
781C22×C4—444no—
782C22×C4—444no—
783C22×C4—444no—
784C22×C4C2×C4×D1112yes—
785C22×C4C2×C4×D1112yes—
786C22×C4C2×C4×D1112yes—
787C22×C4D4×D1112yes—
788C22×C4D4×D1112yes—
789C4⋊C4—444no—
790C4⋊C4—444no—
791C22⋊C4—228no—
792C22⋊C4—228no—
793C22⋊C4—444no—
794C22⋊C4—444no—
795C42—444no—
796C42—444no—
797C11#1387411yescharacteristic, complemented, Sylow
798C23—114no—
799C23—114no—
800C23—114no—
801C23—114no—
802C23—114no—
803C23—114no—
804C23—114no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—222no—
815C23—222no—
816C23—222no—
817C23—222no—
818C23—222no—
819C23—222no—
820C23—222no—
821C23—222no—
822C23—222no—
823C23—222no—
824C23—222no—
825C23—222no—
826C23—222no—
827C23—222no—
828C23—222no—
829C23—222no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23C22×C4×D1111yescharacteristic
834C23C2×D4×D1111yescharacteristic
835C23C2×D4×D1111yescharacteristic
836C23#6703711yescharacteristic
837C23#6704011yescharacteristic
838C23#41×D1111yescharacteristic
839C23#41×D1111yescharacteristic
840C23#41×D1111yescharacteristic
841C23#41×D1111yescharacteristic
842C23#41×D1111yescharacteristic
843C23#41×D1111yescharacteristic
844C23#41×D1111yescharacteristic
845C23#41×D1111yescharacteristic
846C23#6704211yescharacteristic
847C23#6704311yescharacteristic
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—114no—
898C2×C4—114no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—4416no—
921C2×C4—4416no—
922C2×C4—4416no—
923C2×C4—441no—
924C2×C4—441no—
925C2×C4—441no—
926C2×C4—441no—
927C2×C4—441no—
928C2×C4—441no—
929C2×C4—441no—
930C2×C4—441no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—441no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C22—118no—
950C22—224no—
951C22—224no—
952C22—224no—
953C22—224no—
954C22—224no—
955C22—224no—
956C22—224no—
957C22—224no—
958C22—224no—
959C22—224no—
960C22—224no—
961C22—224no—
962C22—224no—
963C22—224no—
964C22D11×#11711yescharacteristic
965C22D11×#11711yescharacteristic
966C22D11×#11711yescharacteristic
967C22C4×D4×D1111yescharacteristic
968C22C4×D4×D1111yescharacteristic
969C22#1062307611yescharacteristic
970C22#1062310311yescharacteristic
971C22D11×#12111yescharacteristic
972C22#1062314111yescharacteristic
973C22#1062314311yescharacteristic
974C22#1062316211yescharacteristic
975C22#1062316211yescharacteristic
976C22#1062316911yescharacteristic
977C22D11×#12311yescharacteristic
978C22#1062318511yescharacteristic
979C22#1062318611yescharacteristic
980C22#1062318611yescharacteristic
981C22#1062319011yescharacteristic
982C22#1062319111yescharacteristic
983C22D11×#12411yescharacteristic
984C22#1062320711yescharacteristic
985C22#1062321011yescharacteristic
986C22#1062322311yescharacteristic
987C22#1062322411yescharacteristic
988C22#1062322411yescharacteristic
989C22D11×#12611yescharacteristic
990C22#1062323611yescharacteristic
991C22#1062323611yescharacteristic
992C22#1062323711yescharacteristic
993C22#1062323711yescharacteristic
994C22#1062323711yescharacteristic
995C22#1062323711yescharacteristic
996C22#1062323811yescharacteristic
997C22#1062323911yescharacteristic
998C22#1062323911yescharacteristic
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—81no—
1005C4—81no—
1006C4—224no—
1007C4—224no—
1008C4—442no—
1009C4—442no—
1010C4—442no—
1011C4—881no—
1012C4—881no—
1013C2—228no—
1014C2#1307101311yescharacteristic
1015C2D11×#38811yescharacteristic
1016C2#1307121511yescharacteristic
1017C2#1307146011yescharacteristic
1018C2#1307146411yescharacteristic
1019C2#1307148211yescharacteristic
1020C2#1307148211yescharacteristic
1021C2#1307208811yescharacteristic
1022C2#1307209611yescharacteristic
1023C2#1307216211yescharacteristic
1024C2#1307217011yescharacteristic
1025C2#1307293711yescharacteristic
1026C2#1307294511yescharacteristic
1027C2#1307299611yescharacteristic
1028C2#1307300411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1443C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1443D11
hypocenterC11#13874
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1443

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
6. #13066878C2semidirect
7. #13066874C2semidirect
8. #13066871C2semidirect
9. #13066851C2semidirect
10. #13066847C2semidirect
11. #13066842C2semidirect
12. #13066840C2semidirect
15. C11×#1443C2semidirect
55. D11×#95C4semidirect
290. #1443D11semidirect
797. C11#13874semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106222772
C2×#106222802
C2×#106222792
C2×D11×#952
#130668782
#130668742
#130668712
#130668512
#130668472
#130668422
#130668402
(C2×D11)⋊#952
C11×#14432
#1387411